{"paper":{"title":"Optimality of a class of entanglement witnesses for $3\\otimes 3$ systems","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jinchuan Hou, Xiaofei Qi","submitted_at":"2013-01-31T09:22:35Z","abstract_excerpt":"Let $\\Phi_{t,\\pi}: M_3({\\mathbb C}) \\rightarrow M_3({\\mathbb C})$ be a linear map defined by $\\Phi_{t,\\pi}(A)=(3-t)\\sum_{i=1}^3E_{ii}AE_{ii}+t\\sum_{i=1}^3E_{i,\\pi(i)}AE_{i,\\pi(i)}^\\dag-A$, where $0\\leq t\\leq 3$ and $\\pi$ is a permutation of $(1,2,3)$. We show that the Hermitian matrix $W_{\\Phi_{t,\\pi}}$ induced by $\\Phi_{t,\\pi}$ is an optimal entanglement witness if and only if $t=1$ and $\\pi$ is cyclic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7558","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}